yes, connect the green safety ground to the chassis. the UL requirements for a ground is to use a separate bolt for the ground (as opposed to a mounting bolt since it's more likely for vibration to loosen the nut due to the mass of the component). of course we use Keps nuts and if they are properly tightened they don't loosen, but requirements don't take that into consideration. you could also strip the cord longer and take the safety ground to the same lug where the yellow transformer wire connects, and this wouldn't require drilling a hole and getting a solder lug, etc.
the device in series with one side of the primary winding (with the thick wire leads) is a thermal protector that opens if the transformer starts heating up due to an overload, disconnecting the power before the temperature would rise enough to destroy the insulation. wire nuts are used since the heat of a soldering iron causes the thermal protector to fail instantly.
installing a three-wire cordset won't cause a GFI or RCB to trip, so works in all situations.
the transformer with two wires was an off-the-shelf Stancor model TP-2 and works only on 115 VAC. we had custom transformers made that are identical in size that had two primary windings so you connect them in parallel for 115 VAC or in series for 230 VAC. (just a note in case someone reads this and finds their transformer has four wires on the primary side).
